Apriori Algorithm

Definition

Apriori algorithm (Agrawal et al. 1996) is a data mining method which outputs all frequent itemsets and association rules from given data.

Input: set $\mathcal{I}$ of items, multiset $\mathcal{D}$ of subsets of $\mathcal{I}$, frequency threshold min_fr, and confidence threshold min_conf.

Output: all frequent itemsets and all valid association rules in $\mathcal{D}$

Method:

• 1: level := 1; frequent_sets : = Ø;

• 2: candidate_sets : = $\{\{i\}\vert i \in \mathcal{I}\}$;

• 3: while candidate_sets ≠ Ø

  • 3.1: scan data $\mathcal{D}$ to compute frequencies of all sets in candidate_sets;

  • 3.2: frequent_sets : = frequent_sets ∪ {C ∈  candidate_sets ∣frequency(C) ≥ min_fr};

  • 3.3: level := level + 1;

  • 3.4: candidate_sets := $\{A\, \subset\, \mathcal{I}\, \mid \mid\, A\, \mid = \mathrm{level\, and}\, B \in\, \mathrm{frequent}\_\mathrm{sets\, for\, all}\, B\, \subset\, A, \, \mid\, B\mid = \text{level} - 1\}$;

• 4: output frequent_sets;

• 5: for each F ∈ frequent_sets

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